Davinci Resolve is, by far, the best free video editing software available
Davinci Resolve: https://www.blackmagicdesign.com/products/davinciresolve/
For guidance, I would look up tutorials for the software you choose on YouTube. Don't focus on specifics right now. (colour grading, audio mixing, compositing, etc.) Just look for hour-long beginner guides that cover everything and follow along leisurely.
You can blow up a video to your screen resolution using most video players. You can also scale up footage in most video editors. Though, keep in mind that in both scenarios, you will probably just be making pixels bigger, leading to image degradation.
Alternatively, you can use Davinci Resolve (free: https://www.blackmagicdesign.com/products/davinciresolve/) to scale up your video. It seems to have a number of resize filters that you can use to approximate what nonexistent pixels would look like (instead of the program just scaling existing pixels up). https://imgur.com/a/kbpamTt
I haven't tried it, but I have played around with its ability to double framerate (by guessing what in-between frames would look like) and it seems to do a pretty alright job with real-life footage.
What are you computer specs? It could just be a slow system, idk. There was a problem in an old build that caused weird freezes, it's been fixed in a recent patch, try updating here if you are on an old version: http://www.videosoftdev.com/free-video-editor/download
A 8700K would give you 6 fast cores which will be great as most applications take advantage of multi-threading these days. 16GB should be fine and an ssd with 4tb hdd also sounds fine. I would take a look at this for the hard drive, you might want to take it out of the external enclosure and put it inside your pc, but it's a great deal and comes with 2mo of Adobe CC Photography (could be useful). Even without that it's still $160 for 8TB of storage.
Depends on what type of editing you're doing. Cutting clips like you said, with no effects or if you run the preview mode 1/4th.
Going lower into the $400 and lower range you want to look for the fastest cpu you can (most ghz), while making sure it's a 4 core cpu. Note that if you do go lower you'll be waiting a long time for things to happen, it will stagger a lot, rendering will take forever, etc. Video editing is a very taxing thing for your pc.